Sentinel Linear Search

Enhancing Search Efficiency with Sentinel Linear Search Algorithm

Sentinel linear search is a modified version of the traditional linear search algorithm that aims to improve its efficiency in certain situations.

In a regular linear search, you iterate through a list or array of elements, comparing each element with the target value until you find a match or reach the end of the list.

Sentinel linear search adds a modification to this process by placing a “sentinel” value at the end of the list to serve as a stopping point for the search.

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Algorithm of Sentinel Linear Search

1. Add the sentinel element (target element) at the end of the list.
2. Start searching from the beginning of the list.
3. Compare the current element with the sentinel.
4. If the current element matches the sentinel, the search is successful, and the index is returned.
5. If the current element doesn’t match, move to the next element and repeat step 3.

Example –

Traditional Linear Search

Suppose input size, n is 4

INPUT – {4, 3, 6, 1}. Target Element is 16

Code for linear search

for (int i = 0; i < size; i++)

{

        if (arr[i] == target) {

            return i; 

        }

}

Iteration 1 – i = 0

Compare i < 4, Yes

Compare 4 == 83, No

Then, i++

Iteration 2 – i = 1

Compare i < 4, Yes

Compare 3==16, No

Then, i++

Iteration 3 – i = 2

Compare i < 4, Yes

Compare 6==16, No

Then, i++

Iteration 4 – i = 3

Compare i < 4, Yes

Compare 1==16, No

Then, i++

Iteration 5 – i = 4

Compare i < 4, No

In Traditional Linear Search, total 9 searches are there.

Time Complexity for comparison – O(2n+1) which reduced to O(n)

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Sentinel Linear Search

Target Element is 16

Suppose input size, n is 4 plus 1 = 5

INPUT – {4, 3, 6, 1, 16}

Code for Sentinel linear search

int i = 0;

    while (arr[i] != target) {

        i++;

    }

Iteration 1 – i = 0

Compare 4 == 16, No

Then, i++

Iteration 2 – i = 1

Compare 3 == 16, No

Then, i++

Iteration 3 – i = 2

Compare 6 == 16, No

Then, i++

Iteration 4 – i = 3

Compare 1 == 16, No

Then, i++

Iteration 5 – i = 0

Compare 16 == 16, Yes

Loop ends.

In Sentinel Linear Search, total 5 searches are there.

Time Complexity for comparison – O(n+1) which reduced to O(n)

Also, the search continues until you find the target value (a match) or until you reach the sentinel value at the end of the list.

When a match is found, you know that the element is present in the list. If you reach the sentinel value without finding a match, you can conclude that the target value is not in the list.

Hence, Sentinel linear search is better than traditional linear search.

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Advantage of Sentinel Linear Search

1. The main advantage of sentinel linear search is that it reduces the number of comparison operations within the loop.
2. In a regular linear search, you would typically have to check if you’ve reached the end of the list on each iteration. With the sentinel value in place, you eliminate this additional comparison, making the search process potentially faster.
3. However, it’s important to note that sentinel linear search is most effective when the search operation dominates the comparison operations. If the list is very small or the comparison operation is highly optimized, the benefits of using a sentinel may be limited.

Complexity of Sentinel Linear Search

1. Time Complexity – In the worst case, the sentinel linear search still performs at O(n), just like the traditional linear search. However, it tends to be faster in practice due to reduced comparisons and optimized loop conditions.
2. Space Complexity – The sentinel approach adds a constant amount of space for the sentinel element, resulting in O(1) space complexity.